The manipulation of two-dimensional materials via their dielectric environment offers novel opportunities to control electronic as well as optical properties and allows one to imprint nanostructures in a noninvasive way. Here we asses the potential of monolayer semiconducting transition-metal dichalcogenides (TMDCs) for Coulomb engineering in a material realistic and quantitative manner. We compare the response of different TMDC materials to modifications of their dielectric surrounding, analyze effects of dynamic substrate screening, i.e., frequency dependencies in the dielectric functions, and discuss inherent length scales of Coulomb-engineered heterojunctions. We find symmetric and rigid-shift-like quasiparticle band-gap modulations for both instantaneous and dynamic substrate screening. From this, we derive short-ranged self-energies for an effective multiscale modeling of Coulomb-engineered heterojunctions composed of a homogeneous monolayer placed on a spatially structured substrate. For these heterojunctions, we show that band-gap modulations on the length scale of a few lattice constants are possible, rendering external limitations of the substrate structuring more important than internal effects. We find that all semiconducting TMDCs are similarly well suited for these external and noninvasive modifications.

• Received 22 December 2019
• Revised 7 August 2020
• Accepted 14 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.115111